The log normal distribution is shown to be useful for characterizing cluster distributions produced by coalescence growth mechanisms. The Smoluchowski equation and variations thereof produce cluster size distributions very similar to those produced using nozzle beam expansions and laser chemistry of organometallics. The model provides a statistically unbiased basis for interpreting cluster size distributions produced using a wide variety of synthetic methods. It also provides a unified chemical and physical basis for discussing and rationalizing the results of a wide range of gas phase cluster experiments. Under certain conditions, size distributions can be produced in which there is an alteration in the number of odd and even clusters produced. In addition to some inferences regarding fullerene chemistry, data gleaned from the literature are rationalized on the basis of the kinematics of cluster formation, the fractal dimension of clusters composed of different atoms, the Periodic Table, and the degree to which the translational motion of the coalescing species is diffusional or ballistic.
We show that gas-phase organometallics can be photolyzed using pulsed UV-visible lasers to initiate synthesis of metal clusters. We use the log-normal distribution function to compare this new method of cluster formation to other methods. Cluster size distributions produced using this new method bear a remarkable similarity to those produced using nozzle beam expansion methods. Although there is deviation from this distribution, these growth methods would seem to involve coalescence growth mechanisms as opposed to Ostwald ripening. Possible reasons for the deviation from a log-natural distribution are suggested. Laser chemistry allows synthesis of gas-phase metal clusters because of the very high pressures of metal atoms attainable using multiphoton dissociation of organometallics.
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